Irreversible deformation with subsequent unloading of a spherical viscoelastoplastic layer

Abstract

Analytic solutions are obtained for a sequence of one-dimensional quasistatic problems describing viscoelastic deformation processes in the material of a hollow ball and the plastic flow nucleation and evolution processes occurring in the ball as the pressure on the outer boundary increases. The unloading process under slow removal of the loading pressure is considered as well. The stress fields and the elastic and plastic strain fields in the spherical layer material, the law of motion of the elastoplastic boundary, and the residual stress level and distribution are computed. It is assumed that at the stage preceding the plastic flow the material obeys the viscoelastic Voigt model and the loading surface is determined by the von Mises plastic flow condition.